4 Answers
4

In the American version published by Scholastic Press in chapter eleven there is the text:

Ron and Hermione joined Neville, Seamus, and Dean the West Ham fan up in the top row. As a surprise for Harry, they had painted a large banner on one of the sheets Scabbers had ruined. It said Potter for President, and Dean, who was good at drawing, had done a large Gryffindor lion underneath. Then Hermione had performed a tricky little charm so that the paint flashed different colors.

and a few lines later:

Out of the corner of his eye he (i.e. Harry) saw the fluttering banner high above, flashing Potter for President over the crowd. His heart skipped. He felt braver.

Annoyingly my niece has my UK edition so I can't check that - can anyone else check to see what text it has?

Anyhow, I don't think there is any great significance to the phrase "Potter for President". It's just meant as encouragement for Harry, and indeed it worked.

I'll check it tonight, that's the earliest I can do anyway :P
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SimonMay 8 '14 at 9:59

4

I checked my copy, English (Philosopher's Stone). Potter for President is there too. I guess Potter for Prime Minister sounds stupid (Dean is a muggle born so would be familiar with Prime Ministers as much as with Minister for Magic and in any case Potter for Minister wouldn't be alliteration, as said below). In seriousness x for President isn't a super-rare saying though mostly used in fun (in the UK at least).
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Mac CooperMay 8 '14 at 15:50

Outside of political associations, "president" is often the title of someone at the head of an organization such as a club, corporation, etc. I don't think this is uncommon enough even in the U.K. as to be unrecognized; Doctor Who, for example, is a British TV show and uses the term "Lord President" for the head of the Time Lords.
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MichaelMay 8 '14 at 16:57

1

I wouldn't say that "Someone for President" is necessarily American flavored.
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NitMay 8 '14 at 23:11

It's nothing related to Quidditch or even the Harry Potter Universe I imagine you read the American Version as it is basically just a chant used for popular and/or successful people. Something along the lines of "We like him so much he should be President" President of the United States of America. Although I don't actually remember that part you're referring to in the books.

I would echo the comments about it being meant as encouragement for Harry, and that the alliteration was snappy.

However I would also add that Hermione, Dean, Seamus and Harry himself all grew up having either one or two Muggle parents or guardians (Ron and Neville are the odd ones out).

"Potter for President" may seem like something that would only make sense to a Muggle or somebody who had been exposed to a Muggle-environment, hence it looks incongruous in the book (I'm not sure we are introduced to any other Wizarding presidents by this point). But if you consider the backgrounds of the characters who made the banner, and the character who it was for (Harry), it explains why they would use these words that might seem more significant to a Muggle than a Wizard.